2002 Nissan Sentra Dashboard going nuts!

Electrical problem
2002 Nissan Sentra 4 cyl Manual 83,000 miles

I recently replaced a bad battery - although, the batttery was only a year old, it still tested bad when I took it out and brought it to Autozone for a test. So, I replaced the battery, but the other day (after driving for about 30 minutes) my battery light and brake light came on in my dashboard. Then, my air bag light began to flicker on and off. Next, I tried my windshiled wipers just to make sure my battery was actually dying and not something else was going crayz and the windshield wipers went incredibly slow. Like a snail was pushing them across my windshield. Then, I turned my headlights off and radio lights off. This turned off the lights on my dashboard for a few seconds, but they soon returned. Oh, and somewhere along the line, my speedometer began to bounce back and forth until it slowly fell to 0mph and my gas gauge fell to E. A month and a half ago, I took my alternator out and tested it because my battery ligth came on, but my battery tested good. Autozone's test said my battery was running good, but when put the alternator back in my car the problem went away. So, with an alternator that is a year old and has recently (a month and a half ago) tested good and with a brand new battery, wheat the heck is going on?